Mister Exam

Other calculators


x/(x-1)^2

Derivative of x/(x-1)^2

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   x    
--------
       2
(x - 1) 
$$\frac{x}{\left(x - 1\right)^{2}}$$
x/(x - 1)^2
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. Apply the power rule: goes to

        The result is:

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   1       x*(2 - 2*x)
-------- + -----------
       2            4 
(x - 1)      (x - 1)  
$$\frac{x \left(2 - 2 x\right)}{\left(x - 1\right)^{4}} + \frac{1}{\left(x - 1\right)^{2}}$$
The second derivative [src]
  /      3*x  \
2*|-2 + ------|
  \     -1 + x/
---------------
           3   
   (-1 + x)    
$$\frac{2 \left(\frac{3 x}{x - 1} - 2\right)}{\left(x - 1\right)^{3}}$$
The third derivative [src]
  /     4*x  \
6*|3 - ------|
  \    -1 + x/
--------------
          4   
  (-1 + x)    
$$\frac{6 \left(- \frac{4 x}{x - 1} + 3\right)}{\left(x - 1\right)^{4}}$$
The graph
Derivative of x/(x-1)^2